1. Field of the Invention
The present invention is directed to scanning probe microscopes, and more particularly, to a method of extracting the tip shape from data obtained by a scanning probe microscope.
2. Description of Related Art
Several known probe-based instruments monitor the interaction between a cantilever-based probe and a sample to obtain information concerning one or more characteristics of the sample. For example, scanning probe microscopes (SPMs), such as the atomic force microscope (AFM), are devices which typically use a sharp tip and low forces to characterize the surface of a sample down to atomic dimensions. More particularly, SPMs monitor the interaction between the sample and the tip on the cantilever of the probe. By providing relative scanning movement between the tip and the sample, surface characteristic data can be acquired over a particular region of the sample, and a corresponding map of the sample can be generated.
The atomic force microscope (AFM) is a very popular type of SPM. The probe of the typical AFM includes a very small cantilever which is fixed to a support at its base and which has a sharp probe tip extending from the opposite, free end. The probe tip is brought very near to or into contact with a surface of a sample to be examined, and the deflection of the cantilever in response to the probe tip""s interaction with the sample is measured with an extremely sensitive deflection detector, often an optical lever system such as described in Hansma et al. U.S. Pat. No. RE 34,489, or some other deflection detector such as strain gauges, capacitance sensors, etc. The probe is scanned over a surface using a high resolution three axis scanner acting on the sample support and/or the probe. The instrument is thus capable of creating relative motion between the probe and the sample while measuring the topography or some other surface property of the sample as described, e.g., in Hansma et al. U.S. Pat. No. RE 34,489; Elings et al. U.S. Pat. No. 5,226,801; and Elings et al. U.S. Pat. No. 5,412,980.
AFMs may be designed to operate in a variety of modes, including contact mode and oscillating mode. In contact mode operation, the microscope typically scans the tip across the surface of the sample while keeping the force of the tip on the surface of the sample generally constant. This effect is accomplished by moving either the sample or the probe assembly vertically to the surface of the sample in response to sensed deflection of the cantilever as the probe is scanned horizontally across the surface. In this way, the data associated with this vertical motion can be stored and then used to construct an image of the sample surface corresponding to the sample characteristic being measured, e.g., surface topography. Alternatively, some AFMs can at least selectively operate in an oscillation mode of operation such as TappingMode.(trademark) (TappingModer(trademark) is a trademark of the present assignee.) In oscillation mode, the tip is oscillated at or near a resonant frequency of the cantilever of the probe. The amplitude or phase of this oscillation is kept constant during scanning using feedback signals, which are generated in response to tip-sample interaction. As in contact mode, these feedback signals are then collected, stored, and used as data to characterize the sample.
Regardless of their mode of operation, AFMs can obtain resolution down to the atomic level on a wide variety of insulating or conductive surfaces in air, liquid or vacuum by using piezoelectric scanners, optical lever deflection detectors, and very small cantilevers fabricated using photolithographic techniques. Because of their resolution and versatility, AFMs are important measurement devices in many diverse fields ranging from semiconductor manufacturing to biological research.
Notwithstanding the fact that scanning probe microscopes are high resolution instruments, the ultimate resolution of the data obtained by such probe-based instruments is limited by the physical characteristics of the tip of the probe itself. More particularly, there are limitations as to how small, and sharp, the tip can be made. In view of this, the tip shape is reflected in the acquired data, a problem that is exacerbated by the fact that AFMs often image very small (e.g., Angstrom scale) features. As a result, an error in the acquired data results and the corresponding accuracy of the surface image is significantly compromised. Hereinafter, the acquired SPM image will periodically be called the xe2x80x9cdilatedxe2x80x9d image.
For some applications, this limitation may be negligible. However, for many applications, the degree of accuracy required to resolve the features of the sample surface is significantly greater, such that tip shape error is unacceptable. For instance, in the semiconductor fabrication industry, imaging features such as lines, trenches and vias with single nanometer accuracy is desired. These features may have dimensions in the range of 120 nm, and are continually getting smaller. With typical tip widths in the range of about 70 nm, the tip shape clearly introduces significant error in the data and must be removed to accurately image the sample surface.
Moreover, the aforementioned problems can be exacerbated by the fact that complex sample surface topologies require a commensurate increase in tip shape complexity to image such surfaces. For example, samples may include undercut regions where a particular x,y scan position may have multiple xe2x80x9cZxe2x80x9d height values (see region xe2x80x9cUxe2x80x9d in FIG. 1, discussed in further detail below). Again, this is common in the semiconductor fabrication industry, and thus tips have been developed to allow imaging of such complex topographies. However, with the increase in tip shape complexity, there typically is a corresponding increase in error in the AFM data.
Two types of known tip shapes are illustrated in FIGS. 1 and 2. Note that probe tips, such as the CD tip, shown in FIG. 2, typically will not have the smooth symmetrical shapes illustrated in the figures. These tip shapes are merely presented as such to highlight the concepts and features of the preferred embodiment. In FIG. 1, a probe tip 10 of a traditional scanning probe microscope includes a parabolic, or other pointed shape that is relatively easy to characterize. Tip 10 includes a shaft 12 and a distal end 14 that although sharp is typically at least slightly rounded at its active surface 15. During a scan (operating in an oscillating mode, for instance), tip 10 interacts with a sample surface 16 to image characteristics of that surface. Tip-sample interaction is controlled, and data is collected, via a control system (not shown) as described previously. The collected data, in turn, may be plotted to image the sample surface. Importantly, this acquired image may not accurately reflect sample surface characteristics due to, among other things, the error introduced by the shape of the pointed tip.
In addition to introducing at least some tip shape error in the acquired data, probe tip 10 is unable to image certain surfaces. In particular, although suitable for many applications, based on its shape probe tip 10 is simply unable to accurately depict vertical sidewalls and undercut regions (which often exist in semiconductor fabrication, for example) in the corresponding sample surface topography. Notably, this is due to limitations in both the tip shape and the algorithms used to control tip position.
To be able to image surface features such as vertical sidewalls and undercut regions, AFMs having more complex probe tips have been developed. In one such instrument, shown in FIG. 2, an AFM employs active X-Z control to follow complex surface topography using a probe tip 20 having a shaft 22 and a distal end 24 including left and right protuberances 26, 28, respectively, in the scan (for example X) direction. By dithering the tip in the scan direction, protuberances 26, 28 are caused to interact with surface features such as vertical sidewalls. As a result, what before caused xe2x80x9cshaded regionsxe2x80x9d (i.e., regions of no tip-sample contact such as undercut region xe2x80x9cUxe2x80x9d illustrated in FIGS. 1 and 2) in the acquired AFM data, now yields at least some data based on tip-sample contact. However, with this increase in flexibility of the types of samples that can be imaged, correcting and reconstructing the image data becomes increasingly difficult.
Overall, whether employing simple or complex probe tip shapes, the problem of the shape of the tip being convolved in the AFM data has been known and appreciated in the art. Although solutions have been attempted with some success, extracting tip shape errors from AFM data has been an inexact process. Moreover, as features become smaller, and because the tip is at least somewhat limited in just how small it can be made, the convolution of the tip in the image data becomes more substantial, and thus it is becoming increasingly important that the tip shape be removed for accurate measurements. Current solutions directed at minimizing tip shape problems provide insufficient accuracy when studying sub-nanoscale features having complex topographies.
In this regard, some known reconstruction techniques have been developed to provide a correction based on characterizing the shape of the tip. Once the tip shape is measured or estimated, it can then be xe2x80x9cerodedxe2x80x9d from the SPM sample image, for example, via mathematical morphology, thus yielding an improved xe2x80x9ccorrectedxe2x80x9d image. This is typically accomplished by removing or eroding the area (2-D; volume for 3-D) of the estimated probe tip shape for each position the probe tip occupies in the scan. However, such techniques are inherently limited. First, removing entire areas (volumes) of tip shape data is highly computationally intensive, even when the tip shape and sample topology are relatively simple adding to system expense and reduces efficiency. In addition, the point of contact of the active surface of the tip changes as the tip traverses a particular topography, and thus the tip shape that should be removed for different points may change, therefore potentially compromising image accuracy.
In general, when working with mechanical probe tips that are manufactured to such small scale, such processes are imperfect, and in any event, the resolution for many cases is unacceptable. And, although more accurate mathematical representations for complex tips and surface topologies are continually being attempted, any such technique will be prohibitively computationally intensive for the applications contemplated by the present invention.
In another known and widely used technique, particularly applicable to the above-described CD probe shown in FIG. 2, rather than applying typical shape xe2x80x9cdeconvolutionxe2x80x9d of the image to compensate for the effect of dilation of the image, a simple subtraction of the tip-width in the scan direction can provide improved reconstructed images and critical dimension measurements.
For this technique to provide a useful correction, the width of the CD tip must be computed to a high degree of accuracy. The way in which this is typically accomplished is by scanning a silicon nanoedge with, for example, the boot shaped CD tip shown in FIG. 2. Because the dimensions of the nanoedge are known or at least very closely approximated, the width of the tip can be extracted from the image data. This scan of a silicon nanoedge is illustrated in FIG. 3A. In particular, a CD tip (for example, 20 in FIG. 2) is scanned from left to right over an improved silicon nanoedge (ISNE) 31 so as to produce an image data profile 30. In this method, the width of the tip is calculated according to,
Wtip=Lxe2x88x92(W1+W2)xe2x80x83xe2x80x83Equation 1 
where xe2x80x9cLxe2x80x9d is the total width of the acquired image a vertical distance xe2x80x9cDxe2x80x9d (defined below) from the plateau. W1 and W2 are defined as follows,
W1=(Dxe2x88x92r) tan xcex1+rxe2x80x83xe2x80x83Equation 2 
and
W2=(Dxe2x88x92r) tan xcex2+r.xe2x80x83xe2x80x83Equation 3 
In these equations, xe2x80x9cDxe2x80x9d is the distance from the plateau xe2x80x9cPxe2x80x9d of the scanned image used for measuring the angles xcex1 and xcex2, as illustrated in FIG. 3. For example, this value may be approximately 800 angstroms. In addition, xe2x80x9crxe2x80x9d is the radius of the vertex of the ISNE, estimated by SEM and/or sharp tip SPM analysis of the nanoedge, and is approximately 75 angstroms. The angles xcex1 and xcex2 are the angles computed from the left and right side slopes, respectively, of the previous tip calibration analysis. Computing the tip width in this fashion, this prior art method can be used to subtract off that width from the image data generated during a scan to approximately correct for the error in the image data. Although providing a correction, this method has significant drawbacks.
First, by simply subtracting the tip width from the image data, it is assumed that the tip-sample contact is being made at a particular point, for example, at the vertical tangent of the protuberances of the boot shaped or CD tip (i.e., at point 29, FIG. 2). However, as the tip scans along a particular topography, the contact point of the tip on the sample translates along the surface of the tip and thus the effective width of the tip at the contact point changes. As a result, a single-valued tip width subtraction is inexact. By simply subtracting off a single value tip-width, an error remains in the reconstructed image as each feature of a unique tip shape cannot be fully accounted for in correcting AFM image data. These errors are directed to inaccuracies in the image of the sample surface shape for both topology and height (vertical error). Another significant drawback is that the width defined in Equations 2 and 3 set forth above are merely estimates for the actual tip width. As the samples to be imaged continue to demand greater resolution, these equations will become inadequate even for those applications where tip-width correction provides an acceptable correction.
Other techniques have been employed; however, each has drawbacks. In short, for the applications contemplated by the present invention, no known technique sufficiently accounts for the tip shape when reconstructing AFM image data.
In view of the above drawbacks with known systems, an improved method was desired to accurately account for tip shapes in dilated SPM data independent of the type of probe tip employed. In addition, the solution should be relatively simple, both to implement and computationally, so as to maximize system efficiency and keep system cost low. More particularly, the AFM field was in need of an improved method that efficiently applies an accurate correction factor to acquired AFM data, i.e., a correction factor that is easy to implement and is based on the actual tip shape as precisely as possible. In addition, for those systems/applications where tip-width subtraction is sufficient, a more precise equation to compute tip-width was desired.
The preferred embodiment overcomes the drawbacks of prior art systems by providing an algorithm that easily analyzes and corrects data from a scanning probe microscope. The invention is directed to an elegant implementation of an algorithm that reconstructs a sample surface from metrology data more accurately and efficiently than prior techniques having the same objective. Importantly, the present invention does so by taking advantage of the geometry of tip-sample contact which heretofore was unappreciated in the art of reconstructing SPM image data. Specifically, when the SPM tip is in contact with the sample, the tangent angle of the tip and the tangent angle of the surface are identical. The inventor exploits this relationship by using the tangent angle of an SPM image or 2D line scan to uniquely determine the point on the tip where contact was made with the sample. If the contact point is known, a tip dimension at this contact point can be used to correct the SPM image. In an alternative embodiment, an improved tip-width correction equation is presented, thus expanding the range of applications for which tip-width correction provides sufficiently accurate resolution. A simplified example of the preferred embodiment will make the general process clear, while more sophisticated details will be discussed later. The example assumes that the size and shape of the tip has been measured, and that a 2-dimensional SPM line scan (like a cross-section through the sample) has been acquired. Further, in this example, assume that the tangent angle at a single point in the SPM line scan is 70 degrees. The outside of the SPM probe can be examined to find a position on the tip that also has a 70 degree tangent angle. As a result, the preferred method exactly locates the contact point on the tip where the specified measurement was made. If there is more than one point on the tip with an angle of 70 degrees, the contact point will be selected by more sophisticated means, detailed later. The next step is to correct the SPM image using the knowledge of the tip contact point. For this, since we know the size and shape of the tip, we can look up or measure tip width at the specified contact point. Using this tip width at the specific contact point, we can correct the measured data and very accurately reconstruct the actual dimensions of the sample.
The preceding example was a simplified 2-dimensional example. In more detail, and generalized for 3-dimensions, the current algorithm analyzes dilated data acquired by a scanning probe microscope to identify a contact point of the tip of the probe on the surface of the sample being imaged. By knowing the contact point of the tip on the sample, an appropriate correction vector can be applied to the raw data, on a point-by-point basis, to reconstruct the surface image. The contact point is determined, preferably, by computing the slope of the raw image data to thereby determine a surface normal associated with the contact point. Note that hereinafter the xe2x80x9ctangent planexe2x80x9d is a mathematical plane that is tangent to the surface at a given point, and the xe2x80x9csurface normal vectorxe2x80x9d is the vector that is perpendicular to the tangent plane. The direction of the unit surface normal vector gives a measure of the local slope of a surface.
According to a first aspect of the preferred embodiment, a method of extracting the shape of a probe tip of a probe-based instrument from data obtained by the instrument is provided. The method generates an image using the data, wherein the data is indicative of a characteristic of a surface of a sample. The method then calculates a slope of the image at a particular region and determines, using the slope, a probe contact point between the tip and the sample at that region.
According to another aspect of this preferred embodiment, the method further includes the steps of translating the image point based on the probe contact point and repeating the above steps for several points in the image data so as to generate a corrected image plot.
In another aspect of this embodiment, the method includes the step of identifying a region of the image where there are at least two points of contact. The method also includes comparing a local curvature of the image to a maximum curvature of the tip. The region of at least two points of contact is where the local curvature exceeds the maximum curvature of the tip.
According to an alternate aspect of the preferred embodiment, a method of correcting tip shape error in data obtained by a scanning probe microscope (SPM) having a tip includes steps of using the SPM to generate the data, wherein the data is indicative of a characteristic of a surface of a sample. Then, the method includes determining a contact point of the tip on the sample at a particular point of the data.
In another aspect of this preferred embodiment, the determining step includes identifying a unit surface normal to the sample at the data point. In addition, the method includes comparing the unit surface normal to tip surface normals associated with corresponding points on an active surface of the tip, wherein the unit surface normal corresponds to a first tip surface normal. Moreover, the tip surface normals each have an associated correction factor. To reconstruct the image profile, the method further includes translating the data point using the correction factor corresponding to the first tip surface normal.
According to a still further aspect of the preferred embodiment, the determining step includes comparing the unit surface normal to tip surface normals associated with several points on an active surface of the tip. In this case, the tip surface normals are non-unique such that the unit surface normal corresponds to at least two of the tip surface normals. As before, the tip surface normals each have an associated correction factor, but in this case, the method includes the step of translating the data point using each of the correction factors associated with at least two tip surface normals.
According to another aspect of this embodiment, the method includes the step of repeating each of the previous steps for data points in a profile generated using the data so as to generate a first reconstructed image profile. The method further includes filtering the first reconstructed image profile so as to generate a second reconstructed image profile. This filtering step preferably includes selecting a point of the first reconstructed image profile that has a minimum Z height for several positions in the first reconstructed image profile.
According to another aspect of the preferred embodiment, a method includes correcting tip shape error in data obtained by a probe-based instrument having a tip. The method includes the step of using the instrument to scan a sample and generate a profile based on the data where the data is indicative of a characteristic of a surface of the sample and includes a plurality of data points. After a contact point of the tip is determined, the method includes determining a correction vector for several points of the data using the corresponding contact point.
According to another aspect of the preferred embodiment, a method includes extracting the width of a tip of a probe-based instrument from data obtained by the instrument. The method includes the steps of using specification end radii (or measuring the radii) of the tip to compute first and second end corrections and correcting the data by subtracting a width of the tip, which is dependent on the first and second end corrections. The first and second end corrections, W1 and W2 are equal to, W1=ABS|-xe2x88x92cos (xcex1) (r+RR)xe2x88x92tan (xcex1) (Dxe2x88x92rxe2x88x92RR+sin (xcex1) (r+RR))+RR and W2=cos (xcex2) (r+RL)xe2x88x92tan (xcex2) (Dxe2x88x92rxe2x88x92RL+sin (xcex2) (R+RL))xe2x88x92RL wherein xe2x80x9crxe2x80x9d is the radius of the silicon nanoedge, xe2x80x9cDxe2x80x9d is a z distance from a plateau of a scanned image to the measured width height, alpha (xcex1) is an angle computed from a left side slope, beta (xcex2) is an angle computed from a right side slope, and RL and Rr are the radii of the left and right sides of the tip, respectively.
These and other objects, features, and advantages of the invention will become apparent to those skilled in the art from the following detailed description and the accompanying drawings. It should be understood, however, that the detailed description and specific examples, while indicating preferred embodiments of the present invention, are given by way of illustration and not of limitation. Many changes and modifications may be made within the scope of the present invention without departing from the spirit thereof, and the invention includes all such modifications.